Fractal and Fractional, Volume 9, Issue 10

Using a Donsker-type construction, we prove the existence of a new class of processes, which we call the self-stabilizing processes. These processes have a particular property: the “local intensities of jumps” vary with the values. Moreov...

In response to the growing complexity of global exploration targets, traditional Euclidean geometric and linear statistical methods reveal inherent theoretical limitations in characterizing hydrocarbon reservoirs as complex geological bodies that exh...

Uncertainty is the biggest issue when modeling real-world multi-level fractional optimization problems. In this paper, a fully intuitionistic fuzzy multi-level multi-objective fractional programming problem (FIF-MLMOFPP) is tackled via two different...

This work investigates how fractionality affects the dynamical behavior of dust-acoustic shock waves that arise and propagate in a depleted-electron complex plasma. This model consists of inertial negatively charged dust grains and inertialess nonext...

With the rise of embodied agents and indoor service robots, object detection has become a critical component supporting semantic mapping, path planning, and human–robot interaction. However, indoor scenes often face challenges such as severe oc...

The aim of this paper is to establish the existence and uniqueness of positive solutions to the non-local Brézis–Oswald-type fractional problems that involve fractional $(r,q)$-Laplace operators and Hardy potentials. In particular, we obse...

In this work, the advection-dispersion model (ADM) is time-fractionalized by the exploitation of Atangana-Baleanu (AB) differential operator to describe contaminant transport in a geological environment. Dispersion, adsorption, and decay, which are k...

In DC microgrids, the combination of pulsed loads and renewable energy sources significantly impairs system stability, especially in highly dynamic operating environments. The resilience and reaction time of conventional proportional–integral (...

The complexity of geological structures significantly impacts both mining production efficiency and operational safety, making its quantitative assessment a core issue in ensuring coal’s safe production and coalbed methane development. Focusing...

The aim of this article is to introduce the distributed-order hyperchaotic detuned (DOHD) laser model. Its dissipative dynamics, invariance, and fixed points (FPs) and their stability are investigated. Numerical solutions of the DOHD laser model are...

We develop a convergence framework for Grünwald–Letnikov (GL) fractional and classical integer difference operators acting on sequences in fuzzy-paranormed (fp) spaces, motivated by data that are imprecise and contain sporadic outliers. Fu...

The primary objective of this study is to provide a more precise and beneficial mathematical model for assessing corruption dynamics by utilizing non-local derivatives. This research aims to provide solutions that accurately capture the complexities...

The goal of this paper is to give an error analysis of a finite difference method for a time-fractional Black–Scholes equation with weakly singular solutions. The time Gerasimov-Caputo derivative is discretized by the L1 scheme on a graded mesh...

Fractional differential equations are used to model complex systems where present dynamics depend on past states. In this work, we study a linear fractional model with two Caputo orders that captures long-term memory together with short-term adaptati...

From a mathematical fantasy to a complex and rigorous mathematical theory, the subject of fractional calculus has applications in diverse and widespread fields of engineering and science, having a rapid growth of its applications [...]

The Yang local fractional setting provides the generalized framework to explore the non-differentiable mappings considering the local properties. Due to the dominance of these concepts, mathematicians have investigated multiple problems, including ma...

This paper presents a novel fractional-order field-oriented control (FO-FOC) strategy for induction motor drives in electric vehicles (EVs) powered by an autonomous photovoltaic (PV) battery energy system. The proposed control approach integrates a f...

Rod-pumping systems represent complex nonlinear systems. Traditional soft-sensing methods used for efficiency prediction in such systems typically rely on complicated fractional-order partial differential equations, severely limiting the real-time ca...

This paper innovatively achieves finite-time modified function projection synchronization (MFPS) for different fractional-order chaotic systems. By leveraging the advantages of radial basis function (RBF) neural networks in nonlinear approximation, t...

The current study explores the fully distributed containment control problem of fractional-order time-delay multi-agent systems by introducing a novel pull-based dynamic event-triggered approach. Firstly, to reduce communication overhead and mitigate...

Hemodynamic management is extremely important in cardiac patients undergoing surgery. Traditionally, the approach towards hemodynamic stabilization included the control of both mean arterial pressure (MAP) and cardiac output (CO) using Sodium Nitropr...

In this work, we numerically investigate the fractional clannish random walker’s parabolic equations (FCRWPEs) and the nonlinear fractional Cahn–Allen (NFCA) equation using the Hybrid Decomposition Method (HDM). The analysis uses the Atan...

Exoskeleton-assisted bodyweight support training (BWST) has demonstrated enhanced neurorehabilitation outcomes in which joint motion prediction serves as the critical foundation for adaptive human–machine interactive control. However, joint ang...

The study of fractals has a long history in mathematics and signal analysis, providing formal tools to describe self-similar structures and scale-invariant phenomena. In recent years, cognitive science has developed a set of powerful theoretical and...

Fractional heat conduction models extend classical formulations by incorporating fractional differential operators that capture multiscale relaxation effects. In this work, we introduce an electrical analogy that represents the action of these operat...

This study introduces a new class of coupled differential systems described by fractal–fractional Caputo derivatives with both constant and state-dependent delays. In contrast to traditional delay differential equations, the proposed framework...

We introduce a class of triply coupled systems of differential equations with fractal–fractional Caputo derivatives and time-dependent delays. This framework captures long-memory effects and complex structural patterns while allowing delays to...

The predator–prey model is a fundamental mathematical tool in ecology used to understand the dynamic relationship between predator and prey populations. This study develops a fractional-order delayed dynamical model for a four-species food web,...

Complex fractal dimensions, defined as poles of appropriate fractal zeta functions, describe the geometric oscillations in fractal sets. In this work, we show that the same possible complex dimensions in the geometric setting also govern the asymptot...

This paper is concerned with the global funnel control (FC) issue of the nonlinear systems with unknown dynamics and time-varying fractional powers. An FC strategy is proposed in this paper, not only the barrier functions but also the tracking and in...

This work presents generalizations and extensions of previous results by incorporating weighted integrals and a refined class of second-type $(h,m)$-convex functions. By utilizing classical inequalities, such as those of Hölder and Young and the P...

By using the Ekeland variational principle and Nehari manifold, we study the following fractional p-Laplacian Kirchhoff equations: $M\left({\left[u\right]}_{s,p}^p+{\int }_{{\mathbb{R}}^N}V\left(x\right){\left|u\right|}^{p}dx\right)[{(-\Delta )}_p^{s}u+$${V\left(x\right)\left|u\right|}^{p-2}u]={\lambda \left|u\right|}^{q-2}u\ln \left|u\right|,x\in {\mathbb{R}}^N,\left(\mathrm{P}\right)$. In these eq...

Fractional differential equations have emerged as a prominent focus of modern scientific research due to their advantages in describing the complexity and nonlinear behavior of many physical phenomena. In particular, when considering problems with in...

In this article, we investigate the regularization and qualitative properties of parabolic Ginzburg–Landau equations in variable exponent Herz spaces. These spaces capture both local and global behavior, providing a natural framework for our an...

This study introduces a novel Fuzzy Piecewise Fractional Derivative (FPFD) framework to enhance epidemiological modeling, specifically for the multi-phasic co-infection dynamics of Omicron and malaria. We address the limitations of traditional models...

Fine-grained sedimentary rocks exhibit significant textural heterogeneity, often obscured by conventional grain size analysis techniques that require sample disaggregation. We propose a non-destructive, image-based grain size characterization workflo...

This paper is devoted to investigating the problem of finite-time (FnT) adaptive cluster synchronization for heterogeneous fractional-order dynamic networks (FODNs) with community structure and co-competition interactions. By designing a suitable ada...

Autonomous robotic navigation is essential in modern systems for revolutionising various industries that operate in both static and dynamic environments. To achieve this autonomous navigation, various conventional techniques that handle environment m...

This work analyzes the behavior of the boundary layer subjected to stresses by obstacles using hourly measurements, in the form of time series, of meteorological variables (temperature (T), relative humidity (RH), and magnitude of the wind speed (WS)...

Fractional calculus shares its historical roots with classical calculus and has lately become a powerful mathematical tool for modeling complex systems [...]

This study investigates the multifractal characteristics and nonlinear cross-correlations between two major carbon credit indices—S&P Global Carbon Index and EEX Global Carbon Index—and key global financial assets: the Euro/US Dollar...

For fractals on Riemannian manifolds, the theory of iterated function systems often does not apply well directly, as these fractal sets are often defined by relations that are multivalued or non-contractive. To overcome this difficulty, we introduce...

This paper analyzes high-frequency intraday Bitcoin data from 2019 to 2022. The Bitcoin market index exhibits two distinct periods, characterized by abrupt volatility shifts. Bitcoin returns can be described by anomalous diffusion processes, transiti...

This paper investigates a class of uncertain fractional-order delayed cellular neural networks (UFODCNNs) with fuzzy operators and nonlinear activations. Both fuzzy AND and fuzzy OR are considered, which help to improve the robustness of the model wh...

This paper presents a systematic methodology for identifying optimal scaling regions in segment-based box-counting fractal dimension calculations through a three-phase algorithmic framework combining grid offset optimization, boundary artifact detect...

In this study, we explore the soliton solutions of the truncated M-fractional fifth-order Korteweg–de Vries (KdV) equation by applying the improved modified extended tanh function method (IMETM). Novel analytical solutions are obtained for the...

This study examines the soliton dynamics in the time-fractional cubic–quintic nonlinear non-paraxial propagation model, applicable to optical signal processing, nonlinear optics, fiber-optic communication, and biomedical laser–tissue inte...

This work investigates the coupled Ivancevic option-pricing model, a nonlinear wave alternative to the Black–Scholes model. By utilizing the recently developed Kumar-Malik method, modified Sardar sub-equation method and the generalized Arnous m...

To investigate the flow characteristics of movable water in coal under the influence of micro-nano pore fractures with multiple fractal structures, this study employed nuclear magnetic resonance (NMR) and multifractal theory to analyze gas–wate...

The theory of stochastic processes is the prominent part of advanced probability theory and very influential in various mathematical models having randomness. One of the potential aspects is to investigate the stochastic convex processes. Working in...